Introduction to Classical Mathematics I: From the Quadratic Reciprocity Law to the Uniformization Theorem

Front Matter....Pages i-xvii
Congruences....Pages 1-10
Quadratic forms....Pages 11-22
Division of the circle (Cyclotomy)....Pages 23-34
Theory of surfaces....Pages 35-43
Harmonic analysis....Pages 44-58
Prime numbers in arithmetic progressions....Pages 59-66
Theory of algebraic equations....Pages 67-89
The beginnings of complex function theory....Pages 90-107
Entire functions....Pages 108-117
Riemann surfaces....Pages 118-136
Meromorphic differentials and functions on closed Riemann surfaces....Pages 137-153
The theorems of Abel and Jacobi....Pages 154-164
Elliptic functions....Pages 165-181
Riemannian geometry....Pages 182-209
On the number of primes less than a given magnitude....Pages 210-218
The origins of algebraic number theory....Pages 219-222
Field theory....Pages 223-231
Dedekind’s theory of ideals....Pages 232-250
The ideal class group and the group of units....Pages 251-261
The Dedekind ς-function....Pages 262-271
Quadratic forms and quadratic fields....Pages 272-280
The different and the discriminant....Pages 281-290
Theory of algebraic functions of one variable....Pages 291-306
The geometry of numbers....Pages 307-312
Normal extensions of algebraic number- and function fields....Pages 313-330
Entire functions with growth of finite order....Pages 331-341
Proof of the prime number theorem....Pages 342-358
Combinatorial topology....Pages 359-377
The idea of a Riemann surface....Pages 378-406
Uniformisation....Pages 407-416
Back Matter....Pages 417-453